Finite Group Databasebeta

← #13075176

Subgroups — #13075176

Order 1408.

680 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66947C211yesmaximal, characteristic, complemented
2C2×#66935C211yesmaximal, characteristic
3C11×#388C211yesmaximal, characteristic, complemented
4#10622607C211yesmaximal, characteristic, complemented
5#10622572C211yesmaximal, characteristic, complemented
6#10622569C211yesmaximal, characteristic, complemented
7#10622568C211yesmaximal, characteristic, complemented
8#10622568C211yesmaximal, characteristic, complemented
9#10622561C211yesmaximal, characteristic, complemented
10#10622553C211yesmaximal, characteristic, complemented
11#10622552C211yesmaximal, characteristic, complemented
12#10622288C211yesmaximal, characteristic, complemented
13#10622288C211yesmaximal, characteristic, complemented
14#10622285C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic, complemented
21C2×C11×C4⋊C4C2211yescharacteristic, complemented
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C42×C11C2211yescharacteristic, complemented
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C2×C4⋊Dic11C2211yescharacteristic, complemented
42C2×Dic11⋊C4C2211yescharacteristic, complemented
43C2×Dic11⋊C4C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45#66947—24no—
46#66935—24no—
47C11×#95C2211yescharacteristic, complemented
48C11×#95C2211yescharacteristic, complemented
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C24×C11C2311yescharacteristic
54C23×D11—22no—
55C23×D11—22no—
56C23×D11—22no—
57C23×D11—41no—
58C23×D11—41no—
59C23×D11—41no—
60C23×D11—41no—
61C23×D11C2311yescharacteristic
62C23×D11C2311yescharacteristic
63C23×D11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—41no—
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44D414yes—
84C2×C4×D11—22no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C11×C4⋊C4—22no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—22no—
90C11×C22⋊C4—41no—
91C42×C11—41no—
92C22⋊Dic11—41no—
93C22⋊Dic11—41no—
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—41no—
108Dic11⋊C4—22no—
109Dic11⋊C4—41no—
110Dic11⋊C4—41no—
111#2697—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11#4112yes—
119C23×C11C2411yescharacteristic
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—44no—
139C22×D11—44no—
140C22×D11—44no—
141C22×D11—44no—
142C22×D11—44no—
143C22×D11—44no—
144C22×D11—44no—
145C22×D11C2×D412yes—
146C22×D11C2×D412yes—
147C22×D11#4112yes—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11C2×D412yes—
166C22⋊D11—44no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182D44—44no—
183D44—44no—
184C4×D11—44no—
185C2×#123—111no—
186C2×#120—111no—
187#397—111no—
188#397—111no—
189#396—111no—
190#396—111no—
191#394—111no—
192#394—111no—
193#390—111no—
194#388—111no—
195#388D1111yescharacteristic, complemented
196#386—111no—
197#386—111no—
198#379—111no—
199#379—111no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11C22×D411yescharacteristic
208C22×C11C2×#4111yescharacteristic
209C22×C11C2×#4111yescharacteristic
210C22×C11H(5,𝔽2)11yescharacteristic
211C22×C11H(5,𝔽2)11yescharacteristic
212C22×C11H(5,𝔽2)11yescharacteristic
213C22×C11H(5,𝔽2)11yescharacteristic
214C2×D11—22no—
215C2×D11—22no—
216C2×D11—22no—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—416no—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C4×C11—22no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—41no—
242Dic11—41no—
243Dic11—41no—
244Dic11—41no—
245Dic11—41no—
246Dic11—41no—
247C25—111no—
248C22×D4—111no—
249C22×D4—111no—
250C22×D4—111no—
251C23×C4—111no—
252#123—224no—
253#120—224no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4C2×D1111yescharacteristic, complemented
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4—111no—
274C2×C22⋊C4C2×D1111yescharacteristic
275C2×C22⋊C4C2×D1111yescharacteristic
276C2×C22⋊C4C2×D1111yescharacteristic
277C2×C42C2×D1111yescharacteristic, complemented
278#95—111no—
279#95—111no—
280#95—111no—
281#95—111no—
282#95C2×D1111yescharacteristic, complemented
283#95C2×D1111yescharacteristic, complemented
284C2×C11—42no—
285C2×C11#53411yescharacteristic
286C2×C11#53811yescharacteristic
287C2×C11#53811yescharacteristic
288C2×C11#54611yescharacteristic
289C2×C11#54611yescharacteristic
290C2×C11#55111yescharacteristic
291C2×C11#56011yescharacteristic
292D11—42no—
293D11—42no—
294D11—42no—
295C24—111no—
296C24—111no—
297C24—111no—
298C24—222no—
299C24—222no—
300C24—222no—
301C24—441no—
302C24—441no—
303C24—441no—
304C24—441no—
305C24C22×D1111yescharacteristic
306C2×D4—114no—
307C2×D4—222no—
308C2×D4—222no—
309C2×D4—222no—
310C2×D4—222no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—441no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—111no—
319C22×C4—111no—
320C22×C4—222no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4C22×D1111yescharacteristic
324C22×C4C22×D1111yescharacteristic
325C22×C4C22×D1111yescharacteristic
326C22×C4C22×D1111yescharacteristic
327C22×C4C22×D1111yescharacteristic
328C22×C4C22×D1111yescharacteristic
329C4⋊C4—22no—
330C4⋊C4—222no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—222no—
338C22⋊C4—222no—
339C22⋊C4—222no—
340C22⋊C4—222no—
341C22⋊C4—222no—
342C22⋊C4—222no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C42—41no—
353C11#269711yescharacteristic, complemented, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—112no—
361C23—112no—
362C23—112no—
363C23—221no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23—221no—
379C23—221no—
380C23—221no—
381C23—444no—
382C23—444no—
383C23—444no—
384C23—444no—
385C23—444no—
386C23—444no—
387C23—444no—
388C23#433912yes—
389C23C23×D1111yescharacteristic
390D4—444no—
391D4—444no—
392D4—444no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—444no—
426C2×C4D4×D1112yes—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—222no—
435C22—222no—
436C22—222no—
437C22—222no—
438C22—222no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22—4416no—
444C22—441no—
445C22—441no—
446C22—441no—
447C22—441no—
448C22—441no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22—441no—
455C22—441no—
456C22C2×#433911yescharacteristic
457C22C2×D4×D1111yescharacteristic
458C22#6703711yescharacteristic
459C22#41×D1111yescharacteristic
460C22#6704211yescharacteristic
461C22#6704211yescharacteristic
462C22#6704211yescharacteristic
463C4—22no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—441no—
470C4—441no—
471C4—441no—
472C4—441no—
473C4—441no—
474C2—42no—
475C2—442no—
476C2—442no—
477C2—442no—
478C2#1062305811yescharacteristic
479C2#1062308111yescharacteristic
480C2#1062309111yescharacteristic
481C2#1062313611yescharacteristic
482C2#1062318811yescharacteristic
483C2#1062320711yescharacteristic
484C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC2×#66935C2
hypercenter#388D11
hypocenterC11#2697
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#66947C2semidirect
3. C11×#388C2semidirect
4. #10622607C2semidirect
5. #10622572C2semidirect
6. #10622569C2semidirect
7. #10622568C2semidirect
8. #10622568C2semidirect
9. #10622561C2semidirect
10. #10622553C2semidirect
11. #10622552C2semidirect
12. #10622288C2semidirect
13. #10622288C2semidirect
14. #10622285C2semidirect
15. #10622278C2semidirect
20. C22×C4×D11C22semidirect
21. C2×C11×C4⋊C4C22semidirect
25. C2×C42×C11C22semidirect
38. C2×(C2×D11)⋊C4C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×C4⋊Dic11C22semidirect
42. C2×Dic11⋊C4C22semidirect
43. C2×Dic11⋊C4C22semidirect
44. C2×Dic11⋊C4C22semidirect
47. C11×#95C22semidirect
48. C11×#95C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
195. #388D11semidirect
258. C2×C4⋊C4C2×D11semidirect
277. C2×C42C2×D11semidirect
282. #95C2×D11semidirect
283. #95C2×D11semidirect
353. C11#2697semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#669472
C2×#669352
C11×#3882
#106226072
#106225722
#106225692
#106225682
#106225612
#106225532
#106225522
#106222882
#106222852
#106222782
#269711